Question: Jessica is 18 years older than Daniel. Five years ago, Jessica was 4 times as old as Daniel. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Daniel. Let Jessica's current age be $j$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $j = d + 18$ Five years ago, Jessica was $j - 5$ years old, and Daniel was $d - 5$ years old. The information in the second sentence can be expressed in the following equation: $j - 5 = 4(d - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = d + 18$ . Substituting this into our second equation, we get the equation: $(d + 18)$ $-$ $5 = 4(d - 5)$ which combines the information about $d$ from both of our original equations. Simplifying both sides of this equation, we get: $d + 13 = 4 d - 20$ Solving for $d$ , we get: $3 d = 33$ $d = 11$.